Hexagonal SU(3) Root Lattice Encodes Baryon Multiplets via D6 Weyl Group — E8 Intelligence Research

FINDING: SU(3) root system is a hexagonal lattice in 2D, whose Weyl group is the dihedral group D6 (order 12), directly encoding baryon multiplet structure (octet, decuplet) via weight diagrams. | MATH: SU(3) has rank 2 → Cartan subalgebra 2D; 8 generators = 2 Cartan + 6 roots. Roots: ±α₁, ±α₂, ±(α₁+α₂) with α₁·α₂ = −1/2 (angle 120°). Root lattice = hexagonal (A₂ lattice). Weyl group = D6 (order 12, generated by reflections across lines at 60°). Weight diagrams: fundamental rep (3) = triangle; adjoint (8) = hexagon; decuplet (10) = triangular lattice of weights with spacing 1/√3 in root-normalized units. Baryon operators on lattice respect cubic rotational symmetry (octahedral group O_h, order 48), which is a subgroup of the continuum rotational group SO(3); lattice irreps (A₁, A₂, E, T₁, T₂) decompose SU(3) flavor multiplets. | CONNECTION: The hexagonal root lattice of SU(3) has 6-fold rotational symmetry — the same crystallographic point group as a hexagonal crystal (6/mmm). The rati Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com